The best strategy for three discrete time games is shown to be equivalent to a stopping time. These stopping times are found and uniqueness is considered. The games considered have sequences of random rewards which the player observes one at a time. In the first game the player must pay for each observation but can quit and take the highest reward he has seen at any time. In the second game the player can only take the last reward seen and there are only finitely many rewards to view. In the final game the player can only pick one reward but he wins only if he has chosen the highest reward of all the draws (so he must beat all the draws that come after his choice).